Assertion:- `Mg^(2+)` is smaller atomic size then `F^(-)`
Resaon :- `Mg^(2+)` has less number of `e^(-)s` than `F^(-)`

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True, but the Reason is False.
D. If both Assertion & Reason are false

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that `Mg^(2+)` is smaller in atomic size than `F^(-)`.
- To evaluate this, we need to consider the atomic structure of both ions.

2. **Analyzing Magnesium Ion (`Mg^(2+)`)**:
- Magnesium (Mg) has an atomic number of 12, which means it has 12 protons and, in its neutral state, 12 electrons.
- When magnesium loses two electrons to form `Mg^(2+)`, it has 10 electrons remaining (12 protons - 2 electrons = 10 electrons).

3. **Analyzing Fluoride Ion (`F^(-)`)**:
- Fluorine (F) has an atomic number of 9, which means it has 9 protons and, in its neutral state, 9 electrons.
- When fluorine gains one electron to form `F^(-)`, it has 10 electrons (9 protons + 1 electron = 10 electrons).

4. **Comparing Electron Configuration**:
- Both `Mg^(2+)` and `F^(-)` have the same number of electrons (10 electrons).
- However, the number of protons differs: `Mg^(2+)` has 12 protons, while `F^(-)` has 9 protons.

5. **Effective Nuclear Charge**:
- The effective nuclear charge is the net positive charge experienced by electrons in an atom. It is calculated as the number of protons minus the shielding effect of inner electrons.
- In `Mg^(2+)`, the 10 electrons are attracted by 12 protons, leading to a stronger effective nuclear charge.
- In `F^(-)`, the 10 electrons are attracted by only 9 protons, resulting in a weaker effective nuclear charge.

6. **Conclusion on Atomic Size**:
- Due to the stronger effective nuclear charge in `Mg^(2+)`, the electrons are pulled closer to the nucleus, resulting in a smaller atomic size compared to `F^(-)`.
- Therefore, the assertion that `Mg^(2+)` is smaller in atomic size than `F^(-)` is correct.

7. **Evaluating the Reason**:
- The reason states that `Mg^(2+)` has fewer electrons than `F^(-)`. This is incorrect because both ions have the same number of electrons (10).
- Thus, the reason is false.

8. **Final Answer**:
- The assertion is true, but the reason is false. Therefore, the correct answer is option C: Assertion true, reason false.